Question

Find the standard form of the equation of the ellipse with the given characteristics.

See image

Answer 1

`((x-4)^2)/(1) +((y-2)^2)/(4) =1`

Explanation:

center of the ellipse (m,n) = (4,2)

distance from center to vertex (a) = 5 - 4 = 1

distance from center to co-vertex (b) = 4 - 2 = 2

Equation of ellipse :
`((x-m)^2)/(a^2) +((y-n)^2)/(b^2) =1`

`((x-4)^2)/(1^2) +((y-2)^2)/(2^2) =1`

`((x-4)^2)/(1) +((y-2)^2)/(4) =1`